There has long been a need to enhance data transmission speed in wireless communications. To address this, work on next-generation data communication standards, such as Long Term Evolution (LTE) has been proceeding. In high-speed data communication standards such as LTE, Multiple Input Multiple Output (MIMO) technology has been attracting attention, since it can apparently increase the bandwidth by transmitting and receiving signals in parallel using multiple antennas at both the transmitting and receiving ends.
In a communication system using MIMO technology, a transmitting apparatus equipped with a plurality of antennas splits one or more data streams into a plurality of signals for transmission. The transmitting apparatus transmits each signal via one of the antennas. On the other hand, a receiving apparatus, which is also equipped with a plurality of antennas, receives the transmitted signals from the transmitting apparatus by the respective antennas. The receiving apparatus then demultiplexes the simultaneously transmitted signals from the signals received by the respective antennas. To demultiplex the transmitted signals, a known method such as Minimum Mean Square Error (MMSE) or Maximum Likelihood Detection (MLD) is used. A receiving apparatus using MLD compares the actually received set of signals with each of the sets of received signals estimated from the sets of candidates for the likely transmitted signals, selects the transmitted signal candidates corresponding to the mostly likely set among the estimated sets, and takes the thus selected signal candidates as the actually transmitted signals. To compare the actually received set of signals with each of the sets of received signals estimated from the sets of transmitted signal candidate, the receiving apparatus using MLD calculates a metric such as the squared Euclidian distance between the two received signal sets.
Compared with a linear demultiplexing method such as MMSE, MLD can achieve excellent reception characteristics. However, the amount of computation that MLD performs in order to demultiplex the transmitted signals from the received signals is larger than the amount of computation that a linear demultiplexing method such as MMSE performs in order to demultiplex the transmitted signals. In particular, in the case of MLD, the number of metric calculations increases exponentially as the number of simultaneously transmitted signals and the number of values that the modulation scheme used for transmission can take increase.
In view of the above, MLD techniques that can reduce the amount of computation have been proposed (for example, refer to: Japanese Laid-Open Patent Publication Nos. 2006-121348 and 2009-33636; K. J. Kim and J. Yue, “Joint channel estimation and data detection algorithms for MIMO-OFDM systems,” in Proc. Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, Nov. 2002, pp. 1857-1861; K. Higuchi, H. Kawai, N. Maeda, and M. Sawahashi, “Adaptive Selection of Surviving Symbol Replica Candidates Based on Maximum Reliability in QRM-MLD for OFCDM MIMO Multiplexing,” Proc. of IEEE Globecom 2004, November 2004, pp. 2480-2486; and M. Siti and M. P. Fitz, “Layered Orthogonal Lattice Detector for Two Transmit Antenna Communications,” in Proc. Allerton Conference on Communication Control and Computing, September 2005).
For example, K. J. Kim and J. Yue describe using QRM-MLD which reduces the number of metric calculations by combining QR decomposition with M algorithm. Suppose that the relationship between N transmitted signals (x0, x1, . . . , xN-1) simultaneously transmitted from a transmitting apparatus and N received signals (y0, y1, . . . , yN-1) received by a receiving apparatus is expressed by the following equation. Here, N is an integer not smaller than 2. Further, the number of transmitted signals need not be the same as the number of received signals, i.e., the number of antennas of the receiving apparatus. As long as the number of antennas of the receiving apparatus is greater than the number of simultaneously transmitted signals, the signals can be transmitted and received using MIMO technology.
                    Y        =                              HX            ⁢                                                  (                                                                                y                    0                                                                                                                    y                    1                                                                                                ⋮                                                                                                  y                                          N                      -                      1                                                                                            )                    =                                    (                                                                                          h                                              0                        ,                        0                                                                                                                        h                                              0                        ,                        1                                                                                                  …                                                                              h                                              0                        ,                                                  N                          -                          1                                                                                                                                                                                h                                              1                        ,                        0                                                                                                                        h                                              1                        ,                        1                                                                                                  …                                                                              h                                              1                        ,                                                  N                          -                          1                                                                                                                                                          ⋮                                                        ⋮                                                        ⋱                                                        ⋮                                                                                                              h                                                                        N                          -                          1                                                ,                        0                                                                                                                        h                                                                        N                          -                          1                                                ,                        1                                                                                                  …                                                                              h                                                                        N                          -                          1                                                ,                                                  N                          -                          1                                                                                                                                )                        ⁢                          (                                                                                          x                      0                                                                                                                                  x                      1                                                                                                            ⋮                                                                                                              x                                              N                        -                        1                                                                                                        )                                                          (        1        )            where the matrix H represents the effective channel matrix describing the correspondence between the transmitted signals and the received signals. In equation (1), noise added to the transmitted signals is omitted for simplicity. In QRM-MLD, the effective channel matrix H is decomposed into a unitary matrix Q and a triangular matrix R, and expressed as shown in the following equation.
                                              ⁢                  H          =                                    QR              ⁢                                                          (                                                                                          h                                              0                        ,                        0                                                                                                                        h                                              0                        ,                        1                                                                                                  …                                                                              h                                              0                        ,                                                  N                          -                          1                                                                                                                                                                                h                                              1                        ,                        0                                                                                                                        h                                              1                        ,                        1                                                                                                  …                                                                              h                                              1                        ,                                                  N                          -                          1                                                                                                                                                          ⋮                                                        ⋮                                                        ⋱                                                        ⋮                                                                                                              h                                                                        N                          -                          1                                                ,                        0                                                                                                                        h                                                                        N                          -                          1                                                ,                        1                                                                                                  …                                                                              h                                                                        N                          -                          1                                                ,                                                  N                          -                          1                                                                                                                                )                        =                                          (                                                                                                    q                                                  0                          ,                          0                                                                                                                                    q                                                  0                          ,                          1                                                                                                            …                                                                                      q                                                  0                          ,                                                      N                            -                            1                                                                                                                                                                                                  q                                                  1                          ,                          0                                                                                                                                    q                                                  1                          ,                          1                                                                                                            …                                                                                      q                                                  1                          ,                                                      N                            -                            1                                                                                                                                                                          ⋮                                                              ⋮                                                              ⋱                                                              ⋮                                                                                                                          q                                                                              N                            -                            1                                                    ,                          0                                                                                                                                    q                                                                              N                            -                            1                                                    ,                          1                                                                                                            …                                                                                      q                                                                              N                            -                            1                                                    ,                                                      N                            -                            1                                                                                                                                              )                            ⁢                              (                                                                                                    r                                                  0                          ,                          0                                                                                                                                    r                                                  0                          ,                          1                                                                                                            …                                                                                      r                                                  0                          ,                                                      N                            -                            1                                                                                                                                                                          0                                                                                      r                                                  1                          ,                          1                                                                                                            …                                                                                      r                                                  1                          ,                                                      N                            -                            1                                                                                                                                                                          ⋮                                                              ⋱                                                              ⋱                                                              ⋮                                                                                                  0                                                              …                                                              0                                                                                      r                                                                              N                            -                            1                                                    ,                                                      N                            -                            1                                                                                                                                              )                                                                        (        2        )            
By multiplying both sides of equation (1) from the left by the Hermitian conjugate QH of the unitary matrix Q, the following equation is obtained.
                    Z        =                                            Q              H                        ⁢            Y                    =                                                    Q                H                            ⁢              QRX                        =                                          RX                ⁢                                                                  (                                                                                                    z                        0                                                                                                                                                z                        1                                                                                                                        ⋮                                                                                                                          z                                                                              N                            -                            1                                                    ⁢                                                                                                                                                                                                    )                            =                                                (                                                                                                              r                                                      0                            ,                            0                                                                                                                                                r                                                      0                            ,                            1                                                                                                                      …                                                                                              r                                                      0                            ,                                                          N                              -                              1                                                                                                                                                                                          0                                                                                              r                                                      1                            ,                            1                                                                                                                      …                                                                                              r                                                      1                            ,                                                          N                              -                              1                                                                                                                                                                                          ⋮                                                                    ⋱                                                                    ⋱                                                                    ⋮                                                                                                            0                                                                    …                                                                    0                                                                                              r                                                                                    N                              -                              1                                                        ,                                                          N                              -                              1                                                                                                                                                            )                                ⁢                                  (                                                                                                              x                          0                                                                                                                                                              x                          1                                                                                                                                    ⋮                                                                                                                                      x                                                                                    N                              -                              1                                                        ⁢                                                                                                                                                                                                                      )                                                                                        (        3        )            where the vector z=(z0, z1, . . . , zN-1) is the unitary transformed vector of the received signal vector which is obtained by the product of the received signal vector Y and the matrix QH. As shown in equation (3), the number of transmitted signals associated with each element of the unitary transformed vector z differs from one element to another. For example, only the transmitted signal xN-1 is associated with the signal On the other hand, N transmitted signal x0 to xN-1 are associated with the signal z0.
The receiving apparatus calculates as the metric the squared Euclidian distance between each of the values of z0 to zN-1 obtained from the actually received signals and each of the values of z0 to obtained by substituting the set of symbol replicas corresponding to the likely transmitted signals into the vector X in equation (3). The symbol replicas are signals tentatively set by the receiving apparatus. In MLD, the receiving apparatus estimates that the set of symbol replicas that minimizes the sum of the metrics obtained for all of z0 to zN-1 represents the actually transmitted signals.
The receiving apparatus using QRM-MLD calculates the metrics for the signals z0 to zN-1 in order of increasing number of transmitted signals associated therewith. For example, in equation (3), the number of transmitted signals associated with the signal zN-1 is the smallest. Accordingly, the receiving apparatus calculates in the first stage the metrics for the signal zN-1, and then calculates in the second stage the metrics for the signal zN-2 which is the second smallest in terms of the number of transmitted signals associated therewith. In the m-th stage, the receiving apparatus calculates the metrics only for M symbol replicas selected in increasing order of the metrics calculated for the signal zm-1 in the immediately preceding stage. For example, suppose that M=3 and that the transmitted signals x0 to xN-1 are modulated by 64-QAM. In this case, there are 64 symbol replicas for each transmitted signal. Then, since only the transmitted signal xN-1 is associated with the signal zN-1, the receiving apparatus first calculates the metrics for the 64 symbol replicas cN-1,0 to cN-1,63 corresponding to the transmitted signal xN-1. Suppose that the symbol replicas corresponding to the three metrics selected in increasing order of the metrics are CN-1,a, CN-1,b, and CN-1,c (where 0≦a, b, c≦63 and a≠b≠c). In this case, the receiving apparatus selects only the three symbol replicas CN-1,a, CN-1,b, and cN-1,c for the transmitted signal xN-1 when calculating the metrics for the signal zN-2. Then, the receiving apparatus calculates the metric for each symbol replica set made up of one of the three symbol replicas CN-1,a, CN-1,b, and CN-1,c and one of the 64 symbol replicas cN-2,0 to CN-2,63 that the transmitted signal xN-2 can take. Since there is no need to calculate the metrics for all the symbol replica sets, the receiving apparatus using QRM-MLD can reduce the amount of computation.
Japanese Laid-Open Patent Publication No. 2006-121348 discloses a technique in which a decision on symbol candidates for a plurality of transmitted signals is made by separately applying the QRM-MLD method to received signals arranged in two different orders and, based on the result of the decision, outputs a plurality of symbol candidates and their likelihood.
K. Higuchi, H. Kawai, N. Maeda, and M. Sawahashi teach an Adaptive Selection of Surviving Symbol replica candidates based on maximum reliability (ASESS) method that can further reduce the number of metric calculations compared with QRM-MLD. In the ASESS method, the receiving apparatus obtains residual received signals at each metric calculation stage by subtracting the signal components of the surviving symbol replica candidates from the received signals obtained by QR-decomposing the channel matrix and thus orthogonalizing the transmitted signals. Then, based on the residual received signals, the symbol replica candidates for which the branch metrics are to be calculated are ranked by the receiving apparatus in increasing order of the expected branch metrics. The receiving apparatus then calculates the branch metrics in sequence starting from the highest ranking symbol replica candidate, and allows only the symbol replica candidates whose branch metrics are smaller than a predetermined threshold value to survive. The ranking of the symbol replica candidates is determined by detecting the quadrant to which the residual received signals belong.
On the other hand, in the Layered Orthogonal Lattice Detector (LORD) method proposed by M. Siti and M. P. Fitz and in the method disclosed in Japanese Laid-Open Patent Publication No. 2009-33636, the receiving apparatus applies QR decomposition to a first channel matrix. Then, based on the upper triangular matrix and unitary matrix obtained by the QR decomposition, the receiving apparatus calculates the metric when some of the plurality of transmitted signals are of a prescribed value. Further, the receiving apparatus generates a second channel matrix by interchanging the order of the channels in the first channel matrix. Then, based on the upper triangular matrix and signal vector Z′ obtained by the QR decomposition of the second channel matrix, the receiving apparatus calculates the metric when some other ones of the plurality of transmitted signals are of a prescribed value. The receiving apparatus then estimates the transmitted signals by determining a set of symbol replicas based on the metric obtained for the first channel matrix and the metric obtained for the second channel matrix.